On friendly index sets and product-cordial index sets of gear graphs

• Published in: AIP Conference Proceedings
• Main Author: Lau G.-C.; Lee S.-M.; Ng H.-K.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics Inc. 2014
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84904704438&doi=10.1063%2f1.4887666&partnerID=40&md5=31d04e95c078dbc1ae4cc20ec7809bd5
• ISSN: 0094243X
• DOI: 10.1063/1.4887666

Let G = (V,E) be a simple connected graph. A vertex labeling of f:V→{0,1} of G induces two edge labelings f+, f*:E→{0,1} defined by f+(xy)x =x f(x)+f(y)(mod2) and f*(xy)x =x f(x)f(y) for each edge xy ε E. For iε{0,1}, let vf(i)x =x |{vεV:f(v)x =x i}|, ef+(i)x =x |{eεE:f+(e)x =x i}| and ef*(i)x =x |eεE:f*(e)x =x i}|. A labeling f is called friendly if |vf(1)-vf(0)|≤1. The friendly index set and the product-cordial index set of G are defined as the sets {|ef+(0)-ef+(1)|:f is friendly} and {|ef*(0)-ef*(1)|:f is friendly}. In this paper, we completely determine the friendly index sets and product-cordial index sets of gear graphs. We also show that the product-cordial indices of a graph can be obtained from its adjacency matrix. © 2014 AIP Publishing LLC.